Is 784 a Prime Number?

There are two types of numbers, mostly — Prime numbers and composite numbers, depending on the number of factors. A prime number is a natural number that is divisible only by 1 and itself. For example, 3 is a prime number because it is divisible by 1 and itself. A composite number is a positive number that is divisible by more than two numbers. For example, 6 is divisible by 1, 2, 3, and 6, making it a composite number. Prime numbers follow a few properties like: - Prime numbers are positive numbers always greater than 1. - 2 is the only even prime number. - They have only two factors: 1 and the number itself. - Any two distinct prime numbers are co-prime numbers because they have only one common factor, which is 1. As 784 has more than two factors, it is not a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 784 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some methods are: - Counting Divisors Method - Divisibility Test - Prime Number Chart - Prime Factorization

The method in which we count the number of divisors to categorize the numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize prime and composite numbers. - If there is a total count of only 2 divisors, then the number would be prime. - If the count is more than 2, then the number is composite. Let’s check whether 784 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 784 by 2. It is divisible by 2, so 2 is a factor of 784. Step 3: Divide 784 by 3. It is not divisible by 3, so 3 is not a factor of 784. Step 4: You can simplify checking divisors up to 784 by finding the square root value. We then need to only check divisors up to the square root value. Step 5: When we divide 784 by 2 and 4, it is divisible by both. Since 784 has more than 2 divisors, it is a composite number.

We use a set of rules to check whether a number is divisible by another number completely or not. It is called the Divisibility Test Method. - Divisibility by 2: The number in the ones' place value is 4, an even number, which means that 784 is divisible by 2. - Divisibility by 3: The sum of the digits in the number 784 is 19. Since 19 is not divisible by 3, 784 is also not divisible by 3. - Divisibility by 5: The unit’s place digit is 4. Therefore, 784 is not divisible by 5. - Divisibility by 7: To check divisibility by 7, double the last digit (4 × 2 = 8). Then, subtract it from the rest of the number (78 - 8 = 70). Since 70 is divisible by 7, 784 is also divisible by 7. - Divisibility by 11: In 784, the sum of the digits in odd positions is 12, and the sum of the digits in even positions is 8. The difference is 4, which is not divisible by 11. Since 784 is divisible by numbers other than 1 and itself, it has more than two factors. Therefore, it is a composite number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, we follow the following steps. Step 1: Write numbers 1 to 1000 in rows and columns. Step 2: Leave 1 without marking, as it is neither prime nor composite. Step 3: Mark 2 because it is a prime number and cross out all the multiples of 2. Step 4: Mark 3 because it is a prime number and cross out all the multiples of 3. Step 5: Repeat this process until you reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 1000. The list does not include 784, so it is a composite number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number. Step 1: We can write 784 as 2 × 392. Step 2: In 2 × 392, 392 is a composite number. Further, break 392 into 2 × 196. Step 3: Break 196 into 2 × 98, and 98 into 2 × 49. Step 4: Finally, 49 is broken down into 7 × 7. Hence, the prime factorization of 784 is 2 × 2 × 2 × 2 × 7 × 7.

Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 784 is a composite number because it is divisible by factors other than 1 and itself. Prime numbers: Numbers greater than 1 that have only two factors, 1 and the number itself, are called prime numbers. Divisibility rules: A set of guidelines to determine if one number is divisible by another without performing division. Perfect square: A number that is the square of an integer. For example, 784 is a perfect square because it is 28 squared. Prime factorization: Breaking down a number into a product of its prime factors.